Entropic characterization of quantum operations

Abstract

We investigate decoherence induced by a quantum channel in terms of minimal output entropy and of map entropy. The latter is the von Neumann entropy of the Jamiolkowski state of the channel. Both quantities admit q-Renyi versions. We prove additivity of the map entropy for all q. For the case q = 2, we show that the depolarizing channel has the smallest map entropy among all channels with a given minimal output Renyi entropy of order two. This allows us to characterize pairs of channels such that the output entropy of their tensor product acting on a maximally entangled input state is larger than the sum of the minimal output entropies of the individual channels. We conjecture that for any channel Φ1 acting on a finite dimensional system there exists a class of channels Φ2 sufficiently close to a unitary map such that additivity of minimal output entropy for Ψ1 x Ψ2 holds.

21 pages, 4 figures

References in corpus (5)

• Universal bounds for the Holevo quantity, coherent information \\ and the Jensen-Shannon divergence
• On Hastings' counterexamples to the minimum output entropy additivity conjecture
• Composition of quantum states and dynamical subadditivity
• Incomplete quantum process tomography and principle of maximal entropy
• Positive maps, majorization, entropic inequalities, and detection of entanglement